You can also gift cities for diplo+.
That's still a trade - and I did mention giving gifts as a bribe.
You can beg for a little something to have 10 turns of guaranteed peace.
Also achieved through bribing...
You can ask/bribe them to change civics or religion, so that they spoil relations with somebody else and improve them with you.
You can, but this falls into the optional category and plays along with roleplaying more than anything. Especially as it's very dependent on the civs' personality how much they care about either. If you don't have one of the two or three civs that care overmuch about religion on your map, this is cut off as a meaningful option. And even where you exercise the civic-switching option, if the AI civ decides it wants good relations with the civ that really hates bureaucrats, it will just change back again after accepting your bribe anyway.
So, it's possible but far from required, and very gamey and counterimmersive.
After Feudalism warring can become tricky. There may be risk that your target will become vassal to some greater power in the course of war, which will bring that power against you. So, when you can't take on more than one enemy at a time, first you must try to isolate your target diplomatically.
All very nice, but relies on you being warlike (since an aggressor will rarely become a vassal unless you not only beat them, but actively invade their territory rather than accepting peace). So this is only relevant when pursuing a military strategy, and moreover when doing so in a context where you don't have overwhelming force - since by the time another civ agrees to become anyone's vassal, you don't usually much care about it and are free to engage a more threatening target. If civs actually agreed to vassalise for protection and political reasons in Civ IV that might work, but as it is AIs only vassalise if they're on the verge of extinction or at least have run out of military forces.
What does it take to befriend potential masters, so they don't take your target as a vassal, or to become pleased/friendly to you, so they can't attack you? And here you juggle civics and religions (if possible), consider giving in to demands, ask/bribe them to change their civics and religion, possibly try to found some city and gift it, so that you finally get to the desired level of relations. And bribing other AIs can be quite expensive, because you can use techs for bribery. You must really weigh pros and cons of catapulting somebody too far ahead. And if you succeed this manipulation against high odds, and your target stands there in the corner alone and in the cold, the satisfaction from all this activity is very big. I see it all as diplomatic activity and it may be quite, erm, 'active'
What this basically amounts to is saying that the Civ IV diplo system gives you good narrative options for engaging in diplomacy if you choose to go down that route, which I believe I already said. Functionally there are still many cases where you simply have no need to do any of that, be it because you're playing non-aggressively, you're the dominant faction, your target is not close enough to any potential threat that it doesn't much matter if they declare war on you, or you simply go to war against your prime targets before Feudalism arises. And as much narrative as you want to inject into it, whether bribing someone not to declare war on you because they're more powerful, or bribing someone not to declare war on you because they might accept a lesser civ as a vassal, in functional terms you're still just ... bribing someone not to declare war on you.
For all the shortcomings in AI behaviour and that BNW introduced mechanically, I'm delighted that Civ V moved away from diplomacy purely being a trade screen in which to obtain bonuses and prevent the other guy declaring war long enough to finish off your current target before moving onto them. That works for Total War (the clue is in the name), but I doubt you'd credit the Total War series as being great exercises in storytelling, let alone examples of sophisticated diplomatic systems in a computer game.
I find that in CiV you can bribe away potential troublemakers much easier, although given enough land, you do run a risk to grow some AI enormity and a big future headache.
I'm more interested in the fact that in Civ V avoiding warfare until you want to kill Civ X is not the primary function of diplomacy, and that as most agreements are bilateral you don't get free bonuses every so often by either exchanging things you need for worthless baubles (except in gold-for-resources trades when this is literally what you're doing, but it's been argued since Civ V released that that ability should be dropped) or simply being strong enough that other civs will randomly pop up to give you presents.
Whatever the older Civ games' strengths - and there are many, both in gameplay and in narrative - the diplomatic system (not just the diplomatic AI) has been atrocious throughout, and I've always been baffled by people who laud it as one of Civ IV's - particularly - selling points. In Civ V the AI is still atrocious, and the new diplomatic system is less AI-friendly to boot, but as an actual framework it's light years ahead of anything else in the series.
In almost every game of Civ 5 I play I'm declaring war on an obnoxious civ that insists on spamming my cities with its Prophets and Missionaries
